International Journal of Fracture

, Volume 59, Issue 2, pp 151–160 | Cite as

A new look at energy release rates for quasistatically propagating cracks in inelastic materials

  • Ralf Peek
  • Xiaomin Deng
Article

Abstract

A mapping technique is used to derive an integral expression for the energy release rate for a quasistatically propagating crack. The derivation does not depend on any assumptions in regard to the contitutive behavior of the material. It leads to a contour integral around the crack tip, plus an area integral over the region enclosed by this contour. Only the stress and displacement fields appear in the integrands. Although for stationary crack solutions known to the authors the area integral is not convergent, for propagating crack solutions in elastoplastic material, the integrals are convergent, and lead to zero energy release rate. This confirms conclusions by Rice from an independent point of view.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A.A. Griffith, Transactions, Royal Society of London, Series A 221 (1920) 163–198.Google Scholar
  2. 2.
    A.A. Griffith, Proceedings, First International Congress of Applied Mechanics, Delft (1924).Google Scholar
  3. 3.
    G.R. Irwin, Fracturing of Metals, American Society for Metals, Cleveland (1948).Google Scholar
  4. 4.
    E. Orowan, Report of Progress in Physics 12 (1949).Google Scholar
  5. 5.
    G.R. Irwin, in Sagamore Conference Proceedings, Vol. II, Syracuse University Press (1956) 289–305.Google Scholar
  6. 6.
    G.R. Irwin, Journal of Applied Mechanics 24 (1957) 361–364.Google Scholar
  7. 7.
    M.L. Williams, Journal of Applied Mechanics 24 (1957) 109–114.Google Scholar
  8. 8.
    J.R. Rice, Journal of Applied Mechanics 35 (1968) 279–386.Google Scholar
  9. 9.
    J.W. Hutchinson, Journal of the Mechanics and Physics of Solids 16 (1968) 13–31.Google Scholar
  10. 10.
    J.R. Rice an G.F. Rosengren, Journal of the Mechanics and Physics of Solids 16 (1968) 1–12.Google Scholar
  11. 11.
    S. Aoki, K. Kishimoto and M. Sakata, Journal of Applied Mechanics 48 (1981) 825–829.Google Scholar
  12. 12.
    L.B. Freund and J.W. Hutchinson, Journal of the Mechanics and Physics of Solids 33 (1985) 169–191.Google Scholar
  13. 13.
    B. Moran and C.F. Shih, Engineering Fracture Mechancs 27 (1987) 615–642.Google Scholar
  14. 14.
    J.C. Amazigo and J.W. Hutchinson, Journal of the Mechanics and Physics of Solids 25 (1977) 81–97.Google Scholar
  15. 15.
    Y.C. Gao and K-C. Hwang, in Proceedings, 5th International Congress of Fracture 2 (1981) 669–682.Google Scholar
  16. 16.
    J.R. Rice, Mechanics of Solids, H.G. Hopkins et al. (eds.), (1982) 539–562.Google Scholar
  17. 17.
    J.R. Rice, in Proceedings, 1st International Congress of Fracture 1 (1966) 309–340.Google Scholar
  18. 18.
    J.R. Rice, in Proceedings, 8th U.S. National Congress of Applied Mechanics, R.E. Kelly ( ed.), Western Periodicals, North Hollywood, California (1979) 191–216.Google Scholar
  19. 19.
    J. Kestin, A Course in Thermodynamics, Vol. II, Hemisphere Publishing (1979).Google Scholar
  20. 20.
    Q.S. Nguyen, in Advances in Fracture Research, D. Francois et al. (eds.), (1981) 2179–2185.Google Scholar
  21. 21.
    Q.S. Nguyen, in Three-Dimensional Constitutive Relations and Ductile Fracture, S. Nemat Nasser (ed.), (1981) 315–330.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Ralf Peek
    • 1
  • Xiaomin Deng
    • 2
  1. 1.College of EngineeringUniversity of MichiganAnn ArborUSA
  2. 2.Department of Mechanical EngineeringUniversity of South CarolinaColumbiaUSA

Personalised recommendations